Gravit. rotational energy related to KE

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SUMMARY

The discussion focuses on a two-particle system with identical masses orbiting around their center of mass. It establishes that the gravitational potential energy (U) of this system is -2 times the total kinetic energy (KE). The relevant equations include KE = 1/2 mv^2 and U = -GMm/r. Participants suggest using centripetal acceleration to derive the velocity (v) necessary for the calculations.

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  • Basic knowledge of Newton's laws of motion
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  • Learn about centripetal force and its relationship to circular motion
  • Explore the implications of energy conservation in orbital mechanics
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katewhitney
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"Consider a system of just two particles, with identical masses, orbiting in circles about their center of mass. SHow that the gravitational potential energy of this system is -2 times the total kinetic energy.

Homework Equations


KE = 1/2 mv^2
U(potential) = -2U(kinetic)
grav. potential =
U=-GMm-r

The Attempt at a Solution


we're supposed to set 1/2mv^2 to the rotational gravitational energy -- but I think i have the wrong equation and I don't know where to go from here...
 
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Welcome to PF!

katewhitney said:
"Consider a system of just two particles, with identical masses, orbiting in circles about their center of mass. SHow that the gravitational potential energy of this system is -2 times the total kinetic energy.

Hi kate! Welcome to PF! :smile:

Hint: find the force on each particle, and balance it with the centripetal acceleration to find v. :wink:
 

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